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On quantum quadratic operators of ${𝕄}_{2}\left(ℂ\right)$ and their dynamics. (English) Zbl 1210.47081
The paper deals with the study of nonlinear dynamics of quantum quadratic operators (q.q.o.) acting on the algebra of $\left(2×2\right)$-matrices ${𝕄}_{2}\left(ℂ\right)$. The authors describe q.q.o. with Haar state as well as quadratic operators with the Kadison-Schwarz property. Using that description, they provide an example of q.q.o. which is not the Kadison-Schwarz operator. Moreover, the stability of the dynamics of q.q.o. is also studied.
##### MSC:
 47H60 Multilinear and polynomial operators 46L30 States of ${C}^{*}$-algebras 81R15 Operator algebra methods (quantum theory) 15A99 Miscellaneous topics in linear algebra 46L60 Applications of selfadjoint operator algebras to physics